Switching H2/H∞ Controller Design for Linear Singular Perturbation Systems


Department of Electrical and Computer Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran Department of Computer Science and Electrical Engineering, Control Engineering Group, Luleå University of Technology, Luleå, Sweden


This paper undertakes the synthesis of a logic-based switching H2/H∞ state-feedback controller for continuous-time LTI singular perturbation systems. Our solution achieves a minimum bound on the H2 performance level, while also satisfying the H∞ performance requirements. The proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. A convex LMI-Based formulation of two fast and slow subsystem controllers leads to a structure which ensures a good performance in both transient and steady-state phases. The stability analysis leverages on the Lyapunov technique, inspired from the switching system theory, to prove that a system with the proposed controller remains globally stable in the face of changes in configuration (controller).


[1] C. Scherer, P. Gahinet and M. Chilali, Multiobjective
outputfeedback control via LMI optimization, IEEE Transaction on
Automatic Control, vol.42, no.7, pp.896-911, 1997.

[2] C. Yi Chen, Hybrid controller design for a mechanical transmission system with variable compliance and uncertainties, International Journal of Innovative Computing, Information and Control, vol.4, no.8, pp.1821-1834, 2008.
[3] Garcia, G., J. Daafouz and J. Bernussou, H2 guaranteed cost control for singularly perturbed uncertain systems, IEEE Trans. on Automatic Control, vol. 43, no. 9, pp.1323-1328, 1998.
[4] Garcia, G., J. Daafouz and J. Bernussou, A LMI solution in the H2 optimal problem for singularly perturbed systems, Proceedings of the American Control Conference, pp. 550-554, Philadelphia, Pennsylvania, June 1998.
[5] E. Gershona, U. Shaked, Static H2 and H∞ output-feedback of discrete-time LTI systems with state multiplicative noise, Systems and Control Letters, vol.55, pp.232-239, 2006.
[6] M. C. de Oliveira, J. C. Geromel, J. Bernussou, An LMI optimization approach to multiobjective controller design for discrete- time system, Proc. of the 38th IEEE Conf. on Decision & Control, Phoenix, Arizona, pp.3611-3616, 1999.
[7] N. Essounbouli, N. Manamanni, A. Hamzaoui, J. Zaytoon, Synthesis of switching controllers: a fuzzy supervisor approach, Nonlinear Analysis, vol.65, pp.1689-1704, 2006.
[8] Kokotovic, P.V., H.K. Khalil, and J. O'Reilly, Singular perturbation methods in control: analysis and design, New York, Academic, 1986.
[9] P. Khargonekar, M. A. Rotea, Mixed H2/H∞ control: a convex optimization approach, IEEE Trans. on Automatic Control, vol.39, pp.824-837, 1991.
[10] R. A. DeCarlo, S. H. Zak, G.P. Matthews, Variable structure control of non-linear multivariable systems: A tutorial, Proc. of the IEEE Conf. on Decision & Control, pp.212-232, 1988.
[11] V. Dragan, T. Morozan, The linear quadratic optimization problem for a class of discrete-time stochastic linear systems, International Journal of Innovative, Computing, Information and Control, vol.4, no.9, pp.2127-2137, 2008.
[12] Pan, Z. and T. Basar, H∞-Optimal control for singularly perturbed systems-Part I:Perfect state measurement, Automatica, vol. 29, no. 2, pp. 401-403, 1993.
[13] Tan, W., T. Leung and Q. Tu, H∞ control for singularly perturbed systems, Automatica, vol. 34, no. 2, pp. 255-260, 1998.
[14] Peres, P.L.D and J.C. Gromel, An alternate numerical solution to the linear quadrautic problem, IEEE Trans. on Automatic Control, vol. 39, no. 1, pp. 198-202, 1994.
[15] Yan Li, J. L. Wang and G. H. Yang, Sub-optimal linear quadrautic control for singularly perturbed systems, Proc. of the 40th IEEE Conf. on Decision and Control, pp. 3698-3703, 2001.
[16] Yan Li, Y. Jiao and X. Wang, Suboptimal H2 static output feedback control for singularly perturbed systems, Proc. of the IEEE Int. Conf. on Automation and Logistics, pp. 2796-2800, 2007.